Question: Marcelle and Jaclyn each think of a polynomial.  Each of their polynomials is monic, has degree 4, and has the same positive constant term and the same coefficient of $z$. The product of their polynomials is \[z^8 +3z^7 +z^6 +3z^5 +4z^4 +6z^3 +2z^2 +4.\]What  is the constant term of Jaclyn's polynomial?
Explanation: Because the constant terms of both polynomials in the product are positive, are the same, and multiply to 4, they must each equal $\sqrt{4} = \boxed{2}$.